Attribute-Based Encryption for Circuits

In an Attribute-Based Encryption (ABE) scheme, a cipher-text is associated with an l-bit public index ind and a message m, and a secret key is associated with a boolean predicate P. The secret key allows to decrypt the cipher-text and learn m i P(ind) = 1. Moreover, the scheme should be secure against collusions of users, namely, given secret keys for polynomially many predicates, an adversary learns nothing about the message if none of the secret keys can individually decrypt the cipher-text. The authors present attribute-based encryption schemes for circuits of any arbitrary polynomial size, where the public parameters and the cipher-text grow linearly with the depth of the circuit.